Sentence examples for matrix mapping from from inspiring English sources

If x ∈ X implies that A x ∈ Y, then we say that A defines a matrix mapping from X into Y and denote it by A : X ⟶ Y.

Then, we say that defines a matrix mapping from into and we denote it by writing if for every sequence the sequence the -transform of is in where (2.1).

Then we say that A defines a matrix mapping from X into Y if for every sequence x ∈ X the A-transform of x exists and is in Y.

Then we say that A defines a matrix mapping from X into Y and we denote it by writing A : X → Y if for every sequence x = ( x k ) k = 0 ∞ ∈ X, the sequence A x = { A n ( x ) } n = 0 ∞, the A-transform of x, is in Y, where A n ( x ) = ∑ k = 0 ∞ a n k x k ( n ∈ N ).

Then we say that A defines a matrix mapping from λ into μ, and we write (A:lambdatomu) if for every sequence (x=(x_{kl})in lambda) the A-transform (Ax={(Ax)_{mn}}_{m,ninmathbb{N}}) of x exists and it is in μ where (Ax)_{mn}=varthetambox sum _{k,l}a_{mnkl}x_{kl}quad text{for each } m,ninmathbb{N}.

If X and Y are subsets of w and (A=(a_{nk})) is an infinite matrix, then A defines a matrix mapping from X into Y, and we denote it by (A:Xto{Y}), if Ax exists and is in Y for all (xin {X}).

In the same year, Mishra [51] gave a characterization of BK-spaces which contain a subspace isomorphic to s c 0 in terms of matrix maps and a sufficient condition for a matrix map from s ℓ ∞ into a BK-space to be a compact operator.

In the following, we will refer to the projection matrix, mapping a 3D point from the world reference system to the image plane Φ j, as M j.

Figure 4(b) shows the GUI of the SNR check, which also includes two panels that display the SNR values at all of the measurement channels(1)) and the correlation matrix map calculated from the whole-brain time signals(2)).

We establish a relation between the notion of an operator of an analytic semigroup and matrix transformations mapping from a set of sequences into, where is either of the sets,, or.

For modelling the friction, we first define the rotation matrix for mapping from the global frame to the local frame of link i (cf. Figure 1) as R i = cos θ i − sin θ i sin θ i cos θ i (12).